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Answer: $7$
To find the next power of $3$, multiply by $3$
To find the last digit of the next power of $3$, multiply the last digit by $3$
$3^1 = 3$ $3^5 = ...3$, since $1\times3=3$
$3^2=9$ $3^6=...9$, since $3\times3=9$
$3^3=...7$ $3^7=...7$ $3^{2011}= ...7$
$3^4=...1$, since $7 \times 3 = 21$ $3^8=...1$ $3^{2012}= ...1$
Powerful Finale
Age 11 to 14
ShortChallenge Level 
Answer: $7$
To find the next power of $3$, multiply by $3$
To find the last digit of the next power of $3$, multiply the last digit by $3$
$3^1 = 3$ $3^5 = ...3$, since $1\times3=3$
$3^2=9$ $3^6=...9$, since $3\times3=9$
$3^3=...7$ $3^7=...7$ $3^{2011}= ...7$
$3^4=...1$, since $7 \times 3 = 21$ $3^8=...1$ $3^{2012}= ...1$
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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